Abstract
We investigate the behaviour of quantum heat engines, in which a qubit is put through the quantum equivalent of the Otto cycle and the heat reservoirs are due to the Unruh effect. The qubit is described by an Unruh-DeWitt detector model coupled quadratically to a scalar field and alternately to a fermion field. In the cycle, the qubit undergoes two stages of differing constant acceleration corresponding to thermal contact with a hot and cold reservoir. Explicit conditions are derived on the accelerations required for this cycle to have positive work output. By analytically calculating the detector response functions, we show that the dimensionality of the quadratic and fermionic coupling constants introduces qualitatively different behaviour of the work output from this cycle as compared to the case in which the qubit linearly couples to a scalar field.
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References
K. Maruyama, F. Nori and V. Vedral, Colloquium: The physics of Maxwell’s demon and information, Rev. Mod. Phys. 81 (2009) 1 [INSPIRE].
T.D. Kieu, The second law, Maxwell’s demon, and work derivable from quantum heat engines, Phys. Rev. Lett. 93 (2004) 140403.
T.D. Kieu, Quantum heat engines, the second law and Maxwell’s daemon, Eur. Phys. J. D 39 (2006) 115.
J.D. Bekenstein, Black holes and the second law, Nuovo Cim. 4 (1972) 737.
J.M. Bardeen, B. Carter and S.W. Hawking, The Four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
S.W. Hawking, Black Holes and Thermodynamics, Phys. Rev. D 13 (1976) 191 [INSPIRE].
N.D. Birrell and P.C.W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press (1984) [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
B.S. DeWitt, Quantum gravity, the new synthesis, in General Relativity; an Einstein Centenary Survey, S.W. Hawking and W. Israel eds., Cambridge University Press (1979) [INSPIRE].
S. Takagi, Vacuum noise and stress induced by uniform accelerator: Hawking-Unruh effect in Rindler manifold of arbitrary dimensions, Prog. Theor. Phys. Suppl. 88 (1986) 1 [INSPIRE].
D. Hümmer, E. Martín-Martínez and A. Kempf, Renormalized Unruh-DeWitt Particle Detector Models for Boson and Fermion Fields, Phys. Rev. D 93 (2016) 024019 [arXiv:1506.02046] [INSPIRE].
A. Sachs, R.B. Mann and E. Martín-Martínez, Entanglement harvesting and divergences in quadratic Unruh-DeWitt detector pairs, Phys. Rev. D 96 (2017) 085012 [arXiv:1704.08263] [INSPIRE].
C.J. Fewster, B.A. Juárez-Aubry and J. Louko, Waiting for Unruh, Class. Quant. Grav. 33 (2016) 165003 [arXiv:1605.01316] [INSPIRE].
L.J. Garay, E. Martın-Martínez and J. de Ramón, Thermalization of particle detectors: The Unruh effect and its reverse, Phys. Rev. D 94 (2016) 104048 [arXiv:1607.05287] [INSPIRE].
B. Reznik, Entanglement from the vacuum, Found. Phys. 33 (2003) 167 [quant-ph/0212044] [INSPIRE].
B. Reznik, A. Retzker and J. Silman, Violating Bell’s inequalities in the vacuum, Phys. Rev. A 71 (2005) 042104 [quant-ph/0310058] [INSPIRE].
G. Salton, R.B. Mann and N.C. Menicucci, Acceleration-assisted entanglement harvesting and rangefinding, New J. Phys. 17 (2015) 035001.
E. Arias, T.R. de Oliveira and M.S. Sarandy, The Unruh Quantum Otto Engine, JHEP 02 (2018) 168 [arXiv:1710.03092] [INSPIRE].
J. Louko and V. Toussaint, Unruh-DeWitt detector’s response to fermions in flat spacetimes, Phys. Rev. D 94 (2016) 064027 [arXiv:1608.01002] [INSPIRE].
A. Satz, Then again, how often does the Unruh-DeWitt detector click if we switch it carefully?, Class. Quant. Grav. 24 (2007) 1719 [gr-qc/0611067] [INSPIRE].
J. Louko and A. Satz, How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile, Class. Quant. Grav. 23 (2006) 6321 [gr-qc/0606067] [INSPIRE].
B.F. Svaiter and N.F. Svaiter, Inertial and noninertial particle detectors and vacuum fluctuations, Phys. Rev. D 46 (1992) 5267 [Erratum ibid. D 47 (1993) 4802] [INSPIRE].
L. Sriramkumar and T. Padmanabhan, Response of finite time particle detectors in noninertial frames and curved space-time, Class. Quant. Grav. 13 (1996) 2061 [gr-qc/9408037] [INSPIRE].
L. Hodgkinson and J. Louko, How often does the Unruh-DeWitt detector click beyond four dimensions?, J. Math. Phys. 53 (2012) 082301 [arXiv:1109.4377] [INSPIRE].
M.E. Peskin and D.V. Schroeder, An Introduction To Quantum Field Theory, Frontiers in Physics, Westview Press (1995).
F. Strocchi, Symmetry Breaking, Lecture Notes in Physics, Springer Berlin Heidelberg (2005) [INSPIRE].
R. Kubo, Statistical mechanical theory of irreversible processes. 1. General theory and simple applications in magnetic and conduction problems, J. Phys. Soc. Jap. 12 (1957) 570 [INSPIRE].
P.C. Martin and J.S. Schwinger, Theory of many particle systems. 1., Phys. Rev. 115 (1959) 1342 [INSPIRE].
R. Balian, D. Haar and J. Gregg, From Microphysics to Macrophysics: Methods and Applications of Statistical Physics, vol. 1, Theoretical and Mathematical Physics, Springer Berlin Heidelberg (2006).
C. Ferreira and J.L. López, Asymptotic expansions of the Hurwitz-Lerch zeta function, J. Math. Anal. Appl. 298 (2004) 210.
E. Freitag and R. Busam, Complex Analysis, Lecture Notes in Mathematics, Springer (2005).
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Gray, F., Mann, R.B. Scalar and fermionic Unruh Otto engines. J. High Energ. Phys. 2018, 174 (2018). https://doi.org/10.1007/JHEP11(2018)174
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DOI: https://doi.org/10.1007/JHEP11(2018)174